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Electronic Colloquium on Computational Complexity

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Reports tagged with Gilbert-Varshamov Bound:
TR22-004 | 3rd January 2022
Silas Richelson, Sourya Roy

Analyzing Ta-Shma’s Code via the Expander Mixing Lemma

Random walks in expander graphs and their various derandomizations (e.g., replacement/zigzag product) are invaluable tools from pseudorandomness. Recently, Ta-Shma used s-wide replacement walks in his breakthrough construction of a binary linear code almost matching the Gilbert-Varshamov bound (STOC 2017). Ta-Shma’s original analysis was entirely linear algebraic, and subsequent developments have ... more >>>

TR22-027 | 22nd February 2022
Guy Blanc, Dean Doron

New Near-Linear Time Decodable Codes Closer to the GV Bound

Revisions: 1

We construct a family of binary codes of relative distance $\frac{1}{2}-\varepsilon$ and rate $\varepsilon^{2} \cdot 2^{-\log^{\alpha}(1/\varepsilon)}$ for $\alpha \approx \frac{1}{2}$ that are decodable, probabilistically, in near linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who ... more >>>

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